Place first 3 ingredients in a large microwave-safe bowl. Cover tightly with plastic wrap, folding back a small edge to allow steam to escape. Microwave at HIGH 8 minutes or until squash is tender; drain. Sprinkle with salt and pepper.
Drain tomatoes well, pressing between paper towels. Stir together tomatoes, chicken, and next 4 ingredients. Layer one-third each soup mixture, squash mixture, breadcrumbs, and Cheddar cheese in a lightly greased 6-qt. slow cooker. Repeat layers twice. Top with Parmesan cheese.
Cover and cook on HIGH 4 hours or until bubbly and edges are golden. Uncover and cook on HIGH 30 minutes. Let stand 10 minutes before serving.